A dead time or a delay element of a filter is present in a controller or a control object in most control systems such as a servo and a process control. FIG. 3 is a block diagram showing an ordinary feedback control system.
In FIG. 3, 2 denotes a main controller (for example, a PID controller), 3 denotes a delay element of the controller, 4 denotes a delay element of a control object and 5 denotes an element having no delay of the control object . In such a control system, the phase of the delay element is delayed. Therefore, the gain of the controller cannot be increased and a sufficient response characteristic cannot be obtained. For this reason, a compensation control for a phase delay is required.
In order to compensate for the phase delay, conventionally, a phase leading compensation element 12 is often added in series as shown in FIG. 4. If Ta and Tb are properly set to be Ta>Tb, the phase of the phase leading compensation element 12 is led and the gain of the main controller 2 is increased so that a control performance can be enhanced.
In the conventional phase compensation control method, however, there has been a problem in that a gain in the high-frequency region of the phase leading compensation element is increased and a high-frequency oscillation is apt to be caused.
Moreover, a dead time is present in the inputs or outputs of most control systems such as a servo and a process control. FIG. 8 is a block diagram showing a conventional feedback control system. In FIG. 8, 22 denotes an ordinary controller (for example, a PID controller) and 23 denotes a control object including a dead time. In such a control system, the phase of a dead time element is delayed. Therefore, the gain of the controller cannot be increased and a sufficient response characteristic cannot be obtained. Therefore, it is necessary to carry out a compensation control for a dead time.
Conventionally, a Smith compensator shown in FIG. 9 has often been used to compensate for a dead time. In FIG. 9, 25 denotes a prediction model of a control object and 26 denotes a dead time element. Taking note of a control input and a feedback signal, a control system in FIG. 9 can be equivalently rewritten as shown in FIG. 6. Referring to FIG. 6, the stability of a feedback system is the same as that of a system having no dead time and the gain of a controller C(s) can be increased so that a control output y can follow a target input r with high precision.
The disturbance removing characteristic of the conventional Smith method will be taken into consideration. Assuming that a disturbance d is present on a control input end as shown in FIG. 10, a transfer function from the disturbance d to the control output y is given as follows.
                                          y            ⁡                          (              s              )                                            d            ⁡                          (              s              )                                      =                                                            P                ⁡                                  (                  s                  )                                            ⁢                              e                                  -                  Ls                                                                    1              +                                                C                  ⁡                                      (                    s                    )                                                  ⁢                                  P                  ⁡                                      (                    s                    )                                                                                +                                                                      C                  ⁡                                      (                    s                    )                                                  ⁢                                  P                  ⁡                                      (                    s                    )                                                  ⁢                                  e                                      -                    Ls                                                                              1                +                                                      C                    ⁡                                          (                      s                      )                                                        ⁢                                      P                    ⁡                                          (                      s                      )                                                                                            ⁡                          [                                                P                  ⁡                                      (                    s                    )                                                  -                                                      P                    ⁡                                          (                      s                      )                                                        ⁢                                      e                                          -                      Ls                                                                                  ]                                                          (        1        )            When the steady value of the control output y for a step disturbance d(s)=1/s is represented by ysd, the following equation can be obtained.
                              y          sd                =                                            lim                              t                →                ∞                                      ⁢                          y              ⁡                              (                t                )                                              =                                                    lim                                  s                  →                  0                                            ⁢                              sy                ⁡                                  (                  s                  )                                                      =                                          lim                                  s                  →                  0                                            ⁢                              {                                                                                                    P                        ⁡                                                  (                          s                          )                                                                    ⁢                                              e                                                  -                          Ls                                                                                                            1                      +                                                                        C                          ⁡                                                      (                            s                            )                                                                          ⁢                                                  P                          ⁡                                                      (                            s                            )                                                                                                                                +                                                                                                              C                          ⁡                                                      (                            s                            )                                                                          ⁢                                                  P                          ⁡                                                      (                            s                            )                                                                          ⁢                                                  e                                                      -                            Ls                                                                                                                      1                        +                                                                              C                            ⁡                                                          (                              s                              )                                                                                ⁢                                                      P                            ⁡                                                          (                              s                              )                                                                                                                                            ⁡                                          [                                                                        P                          ⁡                                                      (                            s                            )                                                                          -                                                                              P                            ⁡                                                          (                              s                              )                                                                                ⁢                                                      e                                                          -                              Ls                                                                                                                          ]                                                                      }                                                                        (        2        )            If C(s) has an integrator, the following equation can be set up.
                              y          sd                =                                            lim                              s                →                0                                      ⁢                          [                                                P                  ⁡                                      (                    s                    )                                                  -                                                      P                    ⁡                                          (                      s                      )                                                        ⁢                                      e                                          -                      Ls                                                                                  ]                                =                      L            ⁢                                                  ⁢                                          lim                                  s                  →                  0                                            ⁢                              sP                ⁡                                  (                  s                  )                                                                                        (        3        )            If P(s) has a pole of s=0, ysd≠0 is obtained. More specifically, in the Smith method, there is a problem in that a steady-state deviation is made for a control object having the pole of s=0. Moreover, if P(s) is unstable in the equation (1), there is a problem in that an output diverges even if any small disturbance is made.